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Beliebt Rechnen >

limit as x approaches 3 of (tan(x-3))/(3e^{x-3)-x}

Lösung

x \to 3 lim (\frac{tan ( x - 3 )}{3 e ^{x - 3} - x})

Lösung

\frac{1}{2}

+1

Dezimale

0.5

Schritte zur Lösung

x \to 3 lim (\frac{tan ( x - 3 )}{3 e ^{x - 3} - x})

Wende das L'Hopital Theorem an

= x \to 3 lim (\frac{sec ^{2} ( x - 3 )}{3 e ^{x - 3} - 1})

Setze den Wert

x = 3

ein

= \frac{sec ^{2} ( 3 - 3 )}{3 e ^{3 - 3} - 1}

Vereinfache

\frac{sec ^{2} ( 3 - 3 )}{3 e ^{3 - 3} - 1} : \frac{1}{2}

= \frac{1}{2}

Graph

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